Black Holes as Geometric Distortional Extrema

It is shown in the present work that the distorted-space model of matter as extended to extreme curvature limits results in characteristics mimicking those of galactic-holes. The distorted-geometry structures exhibit non-Newtonian features wherein the hole or core-region fields of the structures are energetically-repulsive (negative pressure), do not behave functionally in an r-4 manner and terminate at zero at the radial origin (no singularity). Of particular interest is that of r-6 energy-density behavior at structural radial distances near the core of the distortion, a region also displaying potential-well behavior.

Distortional Extrema and Holes in the Geometric Manifold

It is shown in the present work that the distorted-space model of matter as extended to extreme curvature limits results in characteristics mimicking those of galactic-holes. The distorted-geometry structures exhibit non-Newtonian features wherein the hole or core-region fields of the structures are energetically-repulsive (negative pressure), do not behave functionally in an r-4 manner and terminate at zero at the radial origin (no singularity). Of particular interest is that of r-6 energy-density behavior at structural radial distances near the core of the distortion, a region also displaying potential-well behavior.

The Proton and Neutron as Distortional Structures in the Geometric Manifold

It is shown in the present work that the distorted-space model of matter as extended to mimics of the proton and neutron can be described as muonic-based structures. These distorted-geometry structures exhibit non-Newtonian features wherein the hole or core-region fields of the structure (negative pressure core for a positive-charge positive-pressure large-r structure) do not behave functionally in a r−4 manner and terminate at zero at the radial origin (no singularity). Of particular interest is that of r−6 energy-density behavior at structural radial distances near the core of the distortion, a region also displaying potential-well behavior.

Distortional Extrema and Holes in the Geometric Manifold

It is shown in the present work that the distorted-space model of matter as extended to extreme curvature limits results in characteristics mimicking those of galactic-holes. The distorted-geometry structures exhibit non-Newtonian features wherein the hole or core-region fields of the structure are energetically-repulsive (negative pressure), do not behave functionally in an r− 4 manner and terminate at zero at the radial origin (no singularity). Of particular interest is that of r− 6 energy-density behavior at structural radial distances near the core of the distortion, a region also displaying potential-well behavior.

Distortional Extrema and Holes in the Geometric Manifold

It is shown in the present work that the distorted-space model of matter as extended to extreme curvature limits results in characteristics mimicking those of galactic-holes. The distorted-geometry structures exhibit non-Newtonian features wherein the hole or core-region fields of the structure are energetically-repulsive (negative pressure), do not behave functionally in an r-4 manner and terminate at zero at the radial origin (no singularity). Of particular interest is that of r-6 energy-density behavior at structural radial distances near the core of the distortion, a region also displaying potential-well behavior.

DISTORTIONAL EXTREMA AND HOLES IN THE GEOMETRIC MANIFOLD

It is shown in the present work that the distorted-space model of matter as extended to extreme curvature limits results in characteristics mimicking those of galactic-holes. The distorted-geometry structures exhibit non-Newtonian features wherein the hole or core-region fields of the structure are energetically-repulsive (negative pressure), do not behave functionally in an r-4 manner and terminate at zero at the radial origin (no singularity). Of particular interest is that of r-6 energy-density behavior at structural radial distances near the core of the distortion, a region also displaying potential-well behavior.

A density measurement device for solid objects with uneven geometry

Hydrostatic measurement, a method traditionally used to measure the density of solid bodies, is not suitable for all solid bodies. This method is undesirable for solid materials that interact with water and lose their properties. In addition, this method is not suitable for porous objects because measurements in water are erroneous and can damage material samples due to the ability of some solid materials to absorb water. In this study, a new density measurement technique has been developed and evaluated to measure the density of rigid objects by means of nonstandard geometry. The density of objects with distorted geometry was measured pneumatically using communicating vessels logic and using the ideal gas equation. An experiment set has been developed, improved and evaluated. Through this technique, the measurement accuracy of the density of the sample tested was determined with an accuracy of 0.08 %.

Assessment of the Dimensional and Geometric Precision of Micro-Details Produced by Material Jetting

Additive Manufacturing (AM) technology has been increasing its penetration not only for the production of prototypes and validation models, but also for final parts. This technology allows producing parts with almost no geometry restrictions, even on a micro-scale. However, the micro-Detail (mD) measurement of complex parts remains an open field of investigation. To be able to develop all the potential that this technology offers, it is necessary to quantify a process’s precision limitations, repeatability, and reproducibility. New design methodologies focus on optimization, designing microstructured parts with a complex material distribution. These methodologies are based on mathematical formulations, whose numerical models assume the model discretization through volumetric unitary elements (voxels) with explicit dimensions and geometries. The accuracy of these models in predicting the behavior of the pieces is influenced by the fidelity of the object’s physical reproduction. Despite that the Material Jetting (MJ) process makes it possible to produce complex parts, it is crucial to experimentally establish the minimum dimensional and geometric limits to produce parts with mDs. This work aims to support designers and engineers in selecting the most appropriate scale to produce parts discretized by hexahedral meshes (cubes). This study evaluated the dimensional and geometric precision of MJ equipment in the production of mDs (cubes) comparing the nominal design dimensions. A Sample Test (ST) with different sizes of mDs was modeled and produced. The dimensional and geometric precision of the mDs were quantified concerning the nominal value and the calculated deviations. From the tests performed, it was possible to conclude that: (i) more than 90% of all analyzed mDs exhibit three dimensions (xyz) higher than the nominal ones; (ii) for micro-details smaller than 423 m, they show a distorted geometry, and below 212 m, printing fails.

Zeolite encapsulated Ni(ii) Schiff-base complexes: improved catalysis and site isolation

Site isolation and distorted geometry of the zeolite encapsulated complex govern the improved catalysis for phenol hydroxylation reaction.

Planarversusnon-planar: The important role of weak C—H...O hydrogen bonds in the crystal structure of 5-methylsalicylaldehyde

The crystal structure of 5-methylsalicylaldehyde (5-MSA; systematic name 2-hydroxy-5-methylbenzaldehyde), C8H8O2, was discovered to be a textbook example of the drastic structural changes caused by just a few weak C—H...O interactions due to the additional methylation of the aromatic ring compared to salicylaldehydeSA. This weak intermolecular hydrogen bonding is observed between aromatic or methyl carbon donor atoms and hydroxyl or aldehyde acceptor oxygen atoms withd(D...A) = 3.4801 (18) and 3.499 (11) Å. The molecule shows a distorted geometry of the aromatic ring with elongated bonds in the vicinity of substituted aldehyde and hydroxyl carbon atoms. The methyl hydrogen atoms are disordered over two sets of sites with occupancies of 0.69 (2) and 0.31 (2).